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原文摘要

In contrast to a classical bit, which can only take the value $0$ or $1$, its quantum counterpart---a qubit---can exist in a superposition of $0$ and $1$. This is a superposition of data values, and it is then tempting to superpose programs as well. Indeed, a particular superposition of programs, known as the quantum SWITCH, has attracted considerable attention. A natural way to superpose programs is conditional branching on quantum data, and several studies have pursued this idea. However, there is a well-known semantic difficulty with this approach, and the fundamental question of whether the languages proposed in prior work can be physically realised remains open. This paper proposes a physically realisable quantum programming language with quantum branching over quantum channels. We first analyse the semantic difficulty from an implementation perspective and show that the difficulty is caused by arbitrariness in the implementation. We then design a language that is free from this arbitrariness. As expected from its implementation-oriented design, our language is physically realisable. We argue for this from two directions: first, we give a method for compiling programs into quantum circuits; and second, we show that our programs stay within the physically admissible range, namely, that they neither yield probabilities greater than one nor violate causal inequalities. The absence of such violations is established through the inclusion of our language in QC-QC, a notion of realisability studied in physics.